That does depend on how cold the winter is. These plants do well in sheltered coastal gardens in several places in the uk though the mild, wet, south west, particularly Cornwall are particularly conducive for them. How far from the coast are you? Five miles or less is good.

Elsewhere, especially inland where you are more likely to experience colder winter temperatures, you may well be best to keep in containers so that you can move them inside or against the property wall for protection. You could if possible grow them against a south facing wall against your property in a prepared bed too.

I have tried various types of Echium over the years when we were in the UK, in the west, near Bath. We always lost them over the winter, even in the unheated greenhouse.
I would definitely wrap them up in horticultural fleece to protect them from the worst of the frost in mid winter. If you can bring them in, that would be even better. Many of them originate from the Canaries, Madeira and similar places, so are rather tender individuals. But once you get them to flower in the second year, they are really worth it!